Finite Group Databasebeta

← #11799976

Subgroups — #11799976

Order 1152.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592858C211yesmaximal, characteristic
2#10592592C211yesmaximal, characteristic, complemented
3C32×#361C211yesmaximal, characteristic, complemented
4#10589429C211yesmaximal, characteristic, complemented
5#10589380C211yesmaximal, characteristic, complemented
6#10589379C211yesmaximal, characteristic, complemented
7#10589360C211yesmaximal, characteristic, complemented
8#69257—34nomaximal
9C2×C32×D8C2211yescharacteristic
10#64147—21no—
11M16×C3⋊D3—21no—
12C2×#3743C2211yescharacteristic
13C32×M32C2211yescharacteristic
14C32×#108C2211yescharacteristic
15#63659—21no—
16#63649—21no—
17#63646C2211yescharacteristic
18#63644C2211yescharacteristic
19#63639C2211yescharacteristic
20#5159—34no—
21#4893—34no—
22C3×#361D314yescomplemented
23#4563—34no—
24#4514—34no—
25#4513—34no—
26#4494—34no—
27C2×C32×D4—21no—
28C2×#638—41no—
29C2×C4×C3⋊D3D411yescharacteristic
30C32×D8—21no—
31C32×D8—21no—
32C32×M16—21no—
33C2×C32×C8C2311yescharacteristic
34#3757—41no—
35C4⋊(C3⋊Dic3)—21no—
36#3748—21no—
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38#3743—21no—
39#3743—21no—
40#3743—41no—
41C8×C3⋊D3—41no—
42C32×C16—21no—
43C3⋊(C3⋊C16)—21no—
44#2238—91noSylow
45C2×C3×D8C2×D314yes—
46#938—64no—
47D3×M16—64no—
48C2×ΓL(1,𝔽25)—34no—
49C3×M32C2×D314yes—
50C3×#108C2×D314yes—
51#832—64no—
52#822—64no—
53#819—34no—
54#817—34no—
55#812—34no—
56C23×C32—41no—
57C22×C3⋊D3SD1611yescharacteristic
58C32×D4—41no—
59C32×D4—41no—
60C2×C32×C4C2×D411yescharacteristic
61#638—82no—
62C2×C3⋊Dic3—41no—
63C2×C3⋊Dic3SD1611yescharacteristic
64C4×C3⋊D3—21no—
65C4×C3⋊D3—21no—
66C32×C8—41no—
67C32×C8#4111yescharacteristic
68C32×C8#4111yescharacteristic
69C3⋊(C3⋊C8)—21no—
70C3⋊(C3⋊C8)—41no—
71#469—91no—
72#430—91no—
73#365—91no—
74#365—91no—
75#361—91no—
76#361C3⋊D311yescharacteristic, complemented
77#349—91no—
78C2×C3×D4—24no—
79C2×#67—124no—
80C2×C4×D3—34no—
81C3×D8—24no—
82C3×D8—24no—
83C3×M16—24no—
84C2×C3×C8C22×D314yes—
85#217—124no—
86C4⋊Dic3—64no—
87#208—64no—
88C2×C3⋊C8—34no—
89ΓL(1,𝔽25)—64no—
90ΓL(1,𝔽25)—64no—
91ΓL(1,𝔽25)—124no—
92D3×C8—124no—
93C3×C16—24no—
94C3⋊C16—64no—
95C22×C32—81no—
96C22×C32—81no—
97C22×C32—81no—
98C22×C32C2×SD1611yescharacteristic
99C2×C3⋊D3—21no—
100C2×C3⋊D3—41no—
101C32×C4#12311yescharacteristic
102C32×C4AGL(1,ℤ/8)11yescharacteristic
103C3⋊Dic3—21no—
104C3⋊Dic3—81no—
105C2×D8C2×C3⋊D311yescharacteristic
106C2×M16—91no—
107C2×M16—181no—
108#121—181no—
109M32—91no—
110M32C2×C3⋊D311yescharacteristic
111#108—91no—
112#108—181no—
113#108C2×C3⋊D311yescharacteristic
114#106—91no—
115#102—181no—
116C23×C3—44no—
117C22×D3—34no—
118C3×D4—44no—
119C3×D4—44no—
120C2×C3×C4D3×D414yes—
121#67—248no—
122C2×Dic3—34no—
123C2×Dic3—124no—
124C4×D3—64no—
125C4×D3—64no—
126C3×C8—44no—
127C3×C8#23514yes—
128C3×C8#23714yes—
129C3⋊C8—64no—
130C3⋊C8—124no—
131C2×C32—21no—
132C2×C32—161no—
133C2×C32#48111yescharacteristic
134C3⋊D3—41no—
135C2×D4—21no—
136C2×D4—361no—
137C22×C4—91no—
138D8—21no—
139D8—21no—
140M16—21no—
141M16—181no—
142M16—181no—
143M16—181no—
144M16—361no—
145C2×C8—91no—
146C2×C8—361no—
147C2×C8C22×C3⋊D311yescharacteristic
148C4⋊C4—181no—
149C22⋊C4—361no—
150C16—21no—
151C16—181no—
152C22×C3—84no—
153C22×C3—84no—
154C22×C3—84no—
155C22×C3D3×SD1614yes—
156C2×D3—64no—
157C2×D3—124no—
158C3×C4#88314yes—
159C3×C4#91114yes—
160Dic3—64no—
161Dic3—244no—
162C32#223811yescharacteristic, complemented, Sylow
163C23—41no—
164C23—91no—
165D4—41no—
166D4—41no—
167D4—722no—
168C2×C4—91no—
169C2×C4—181no—
170C2×C4—181no—
171C2×C4—361no—
172C2×C4D4×C3⋊D311yescharacteristic
173C8—41no—
174C8—181no—
175C8—361no—
176C8#382811yescharacteristic
177C8#383011yescharacteristic
178C2×C3—24no—
179C2×C3—164no—
180C2×C3#477714yes—
181D3—124no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—181no—
186C22—361no—
187C22SD16×C3⋊D311yescharacteristic
188C4—181no—
189C4—721no—
190C4#6409211yescharacteristic
191C4#6412011yescharacteristic
192C3#6925714yescomplemented
193C2—21no—
194C2—161no—
195C2—361no—
196C2#1059247611yescharacteristic
subgroupG/H
centerC2#10592476
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#361C2
socleC2×C32#481
prime radical#10592858C2
hypercenter#361C3⋊D3
hypocenterC32#2238
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10592592C2semidirect
3. C32×#361C2semidirect
4. #10589429C2semidirect
5. #10589380C2semidirect
6. #10589379C2semidirect
7. #10589360C2semidirect
22. C3×#361D3semidirect
76. #361C3⋊D3semidirect
162. C32#2238semidirect
192. C3#69257semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105928582
#105925922
C32×#3612
#105894292
#105893802
#105893792
#105893602
#692573